Strategies for buyers

OpeningRight direction, money gone

You think stock X (now $100, IV 30%) will rise to 105 within a month. To get “maximum leverage,” you buy 10 of the 30-day 105 calls at $1.66 each, $1,662 in total.

Two weeks later the stock is at 104. You open your account: the calls are worth only $1.88, a gain of just 13%. While the stock rose, IV fell from 30% to 26%, and 14 days of time value drained away. On expiration day the stock closes at 104.5, up 4.5% from when you bought. You were completely right on direction, yet your 105 calls are worthless and the whole $1,662 is gone.

The third row is priced on day 30 with IV at 26% and 60 days left. It made less than the 30-day ATM calls, but it still has 60 days to run: if the view keeps playing out, the position is still alive. The first row has three problems: the strike is too far out of the money, the expiration is too close, and it ignored the chance that IV would fall. This chapter starts from those three problems. First come the buyer's three enemies (7.1), then how to choose the strike (7.2), expiration (7.3), timing (7.4) and structure (7.5, 7.6), and finally a list of mistakes and the management rules.

7.1The buyer's three enemies

Every day, a buyer fights three enemies: time, IV compression and being wrong on direction. To make money, the price move has to be big enough and fast enough to overpower the other two.

Take a 30-day ATM call (3.591) and break down its P&L. Ten days later the stock is up 3% and IV has dropped from 30% to 26%; the option is now 4.398, a 22% gain. Reprice one factor at a time, in this order—price, then time, then IV:

Direction contributed 50%, and the two enemies, time and IV, took back 55% of that. Change the order of the breakdown (time first) and the time term becomes −0.682. The numbers shift slightly; the conclusion doesn't.

Enemy 1: time

An ATM option's daily Theta is about 0.062, or 1.74% of the premium. If the stock doesn't move, this option is down to 70% of its value after 15 days. Time decay isn't steady: it speeds up as expiration approaches (Table 7-14 in Section 7.9).

Enemy 2: IV compression

Vega is about 0.114: every 1-point drop in IV takes 0.114 off the option. The most dangerous case is the IV crush after an event (Chapters 5 and 6). There is also an easily overlooked pattern: for stock indexes and many large-cap stocks, IV tends to fall when prices rise and rise when they fall. Call buyers often find IV dropping just as their view comes true.

Enemy 3: wrong direction, or “not right enough”

A buyer has to be right not only on direction but on size. The breakeven at expiry is the strike plus the premium. For the 30-day ATM call it is 103.59: the stock has to rise 3.59% just to avoid a loss.

Using Black-Scholes risk-neutral probabilities, this ATM call has a 49.8% chance of finishing in the money, and only a 33.9% chance of finishing above breakeven. A buyer's win rate is naturally below one half; the buyer relies on winning big when they do win. These probabilities are implied by market prices and ignore the stock's true expected return, but they are good enough as an approximation.

Which enemy is most dangerous depends on what you bought

So the first step in controlling the three enemies is to identify which one this trade fears most, then weaken it with your choice of strike, term and structure. The next four sections cover those tools.

7.2Strike: Delta 30, 50, 70

The strike decides what you are betting on: an ITM option is mainly a bet on direction, an ATM option on direction plus size, and an OTM option on size plus speed.

Compare them on a concrete view: the stock is at $100 and you think it will rise 10% within three months. Take three 90-day calls with strikes where Delta is about 0.70, 0.50 and 0.30 (94, 102 and 110):

The leverage row uses elasticity: if the stock rises 1%, the option rises roughly Δ × S / C percent. The OTM option has the most leverage, but its daily time decay and IV risk (as a share of premium) are also three to four times those of the ITM option.

Look at it another way: with the same $1,000, how much exposure does each strike buy?

For the same money, the OTM call gets 57% more directional exposure (113 shares vs. 72). The price is 3.3 times the daily time decay and 3.7 times the IV exposure of the ITM call. The extra directional exposure isn't enough to offset the other two. That is why “buy OTM when money is tight” is a common but costly habit.

The highlighted row matters most. Your view is “up 10%,” and the Delta 30 strike sits right at 110. If you are exactly right and the stock finishes at 110, this option goes to zero. An OTM option is a bet that the stock rises “more than your target”; its breakeven is 112.73. Conversely, the sooner the move comes, the better the OTM option does: if the stock reaches 110 the day you buy, it makes 158%.

How to choose

• Confident on direction, unsure on timing: Delta 0.60–0.75. It behaves like a stock with a built-in stop-loss, and time decay is a small share of the price.
• A clear catalyst, with a big move expected soon: Delta 0.40–0.50.
• Delta below 0.30: use it only when you expect a rise far beyond your target, and soon. Size it like a lottery ticket.

A simple check: the target must be well above breakeven, and when you reprice the option on the date you expect the move, as in Table 7-3, the return has to be enough to pay you for the risk you are taking.

7.3Expiration: build in a buffer

Buy more time than you expect the move to take. A rule of thumb is 1.5 to 2 times your expected timeframe, or at least 30 extra days.

There are three reasons. First, timing is usually the least reliable part of any view. Second, time decay is fastest in the final month. Third, extra time isn't expensive: the longer the term, the lower the cost per day.

The 120-day option costs 2.1 times as much as the 30-day option but buys 4 times the time, and its cost per day is only 54% of the 30-day option's. This is the square-root rule at work: an ATM option's price is roughly proportional to √T, so 4 times the time only about doubles the price.

Where 1.5 to 2 times comes from

The multiple is a compromise between two constraints, not a rigorous derivation. First, by the numbers in Section 7.9, an option loses value fastest in the last third of its life, and you want to be well clear of that stretch when your view plays out; buy twice the time and you still have half of it left when that happens. Second, buying too much time means paying for more Vega and tying up more capital: doubling the term raises the premium by about 44% (close to √2, with the small extra coming from interest). 1.5 to 2 times falls between the two.

It doesn't apply in three cases: when you are trading a specific event (such as earnings), where what you want is the nearest expiration that covers that day; when back-month IV is clearly higher than front-month IV; and when capital is limited, in which case buy fewer contracts rather than a shorter term.

Rolling: buy more time

If your view hasn't played out but the option is close to expiring, you can roll: sell the near-month option you hold and buy a later expiration. Example: the 90-day 102 call from Section 7.2 (5.48). On day 60 the stock is at 104 with 30 days left; the option is worth 4.82, of which 2.82 is time value, and it still loses 0.063 a day.

• Roll to a new 90-day 104 call (ATM, Δ 0.56): price 6.67, an extra 1.85 per share.
• Roll to a new 90-day 106 call (Δ 0.51): price 5.74, an extra 0.92 per share.

On paper a roll looks like one trade, but it is really two: close the old position (realizing the gain or loss) and open a new one. The new position has to pass this chapter's tests again: is the target above the new breakeven, is IV reasonable, is there enough time? If you wouldn't buy it as a fresh trade today, don't buy it in the name of a roll. Above all, don't roll just to avoid “realizing a loss.” That only postpones the loss and makes it bigger.

7.4Timing: watch IV

Buy options when IV is high and you prepay for a lot of movement while also carrying the risk that IV falls. Buy when IV Rank is low and a rebound in IV becomes an extra tailwind.

An ATM option's Vega barely changes with IV, so every 1-point move in IV has the same dollar impact. The difference is direction: when IV is high relative to its own history, it is more likely to come down (mean reversion, Chapter 6); when it is low, it is more likely to go up.

The same +5% earns only 13% in the first row. If you buy at IV 45% and IV drops to 33%, the stock has to rise 3.75% just to break even. The last row is the reverse: with IV going from 22% to 26%, even if the stock doesn't move at all, the option is worth 3.40 after 10 days, more than the 3.33 you paid.

A second yardstick: IV vs. RV

IV Rank tells you where IV sits in its own history. The ratio of IV to RV tells you whether options are expensive relative to how much this stock is actually moving right now. As Chapter 4 showed, a 30-day ATM option at IV 30% needs the stock to move about $1.64 per calendar day for Gamma to earn back Theta. If the stock's 20-day RV is only 22%, its average one-standard-deviation move per calendar day is only $1.15. Unless you have a strong directional view, this option is most likely losing money slowly. For a buyer, the ideal combination is a low IV Percentile and IV no higher than recent RV.

When IV is high but you still want to be bullish

• Switch to a debit spread: the leg you sell is also priced at high IV, so most of the Vega cancels out (Section 7.5).
• Avoid the event: if IV is high because of earnings, choose a contract that expires before the report, or wait until IV falls after the report and then buy.
• Change the underlying: express the same view with a sector ETF, or with a highly correlated stock that has lower IV.
• Switch to the selling side: high IV is itself an edge for sellers, for example selling cash-secured puts (Chapter 8).

The minimum check before you trade: IV Percentile below 50, ideally below 30; IV not clearly above 20-day RV; and is there an event before expiration, and where will IV fall to after it?

7.5Debit spreads

A debit spread means buying one option while selling a further OTM option of the same type and expiration. A call debit spread is also called a bull call spread: it costs less, caps the gain and shrinks Vega and Theta exposure sharply.

Compare a 90-day long 100 call with the spread “buy the 100 call, sell the 110 call”:

A spread is worth the difference between its two options. The 110 call you sold also has Theta and Vega, with the opposite sign, so the spread's Theta is only 15% of the long call's and its Vega only 11%: if IV drops 5 points, the long call loses 0.98 and the spread just 0.11. The cost is that Delta is also down to 44%: in a sharp short-term rally the spread gains more slowly, and it can only make money up to 110.

Where to put the short leg

The rule is simple: put the short leg at your target price. Your view is a rise to 110, so gains above 110 were never part of your plan. Selling them to lower your cost is the cheapest concession you can make. The narrower the spread, the more it behaves like a bet on a range and the less sensitive it is to IV and time; the wider it is, the closer it gets to a long call.

Long call or spread: four questions

1. Do you have a clear target price? If yes, lean toward a spread with the short leg at the target. If not, and you just think it “will go up a lot,” lean toward the long call.
2. Is IV high relative to its own history? If so, lean toward a spread and let the short leg absorb part of the IV decline.
3. How fast do you expect the move? For a sharp rally within days, the long call's Delta and Gamma help more; for a slow climb over months, the spread's low Theta helps more.
4. Is there an event before expiration? If so, the spread's small Vega limits the damage from the post-event IV crush.

If three of the four questions point to a spread, use the spread. It is a crude rule, but it stops you from overpaying just because “a long call has no cap.”

The bearish mirror: put debit spreads

For a bearish view the structure is fully symmetric: buy the higher-strike put and sell the lower-strike put. A 90-day 100/90 put spread costs 3.66, with a max profit of 6.34 and breakeven at 96.34; a long 100 put alone costs 5.43, with breakeven at 94.57. The spread's Theta is 24% of the long put's and its Vega 30%. These ratios are a little higher than for the call spread because, on a log scale, 90 is further from the money than 110, so the short leg offsets less.

The hassles of spreads

• Enter it as one order: if the two legs fill separately, a price move in between can leave you holding one naked side. Make sure the order ticket shows a single “spread order” with both legs filling together.
• You pay the bid–ask spread on two legs to close: on illiquid options, the round-trip cost can eat a large part of your profit.
• The stock finishes between the two strikes at expiry: the long leg is exercised, the short leg expires worthless, and on Monday you hold stock. Close the position yourself as expiration nears; don't leave it to the last minute.
• Gains come slowly: a spread only gets close to its maximum value near expiration. If the stock reaches 115 by day 30, the spread is up just 107%, well short of the theoretical maximum of 172%, because the short leg still has time value.

7.6LEAPS: options as a stock substitute

A deep ITM call with more than a year to expiration and a Delta of 0.70–0.80 (LEAPS) gives you close to 80% of the stock's exposure for a little over 20% of the capital. The cost is some time value, which equals exactly “interest on borrowed money” plus “a protective put.”

Example: stock at 100, a one-year 85 call priced at 22.35, Delta 0.795. Intrinsic value is 15, time value 7.35. One contract costs $2,235 and gives you exposure to about 80 shares; buying 100 shares outright costs $10,000.

What the time value actually buys

Start from put–call parity, C = S − Ke^−rT + P, and move the intrinsic value S − K to the left side:

Plug in the numbers: the 85 put is worth 4.02, the interest is 85 × (1 − e^−0.04) = 3.33, and together they make 7.35, exactly the time value. So buying LEAPS does three things at once: buy the stock, borrow $85 (paying 4% interest) and buy an 85 put for protection. If what you wanted all along was a long position that “can lose at most down to 85,” LEAPS are a prepackaged way to hold it.

Two ways to use the same $10,000

A: buy 100 shares. B: buy 1 LEAPS contract and put the remaining $7,765 in T-bills at 4% (continuously compounded), about $317 over a year.

Above 85, B makes $418 less than A: that is the cost of the “protective put” plus the interest difference. Below 85, B's loss is capped at $1,918. If the stock falls 30%, A loses $3,000 and B only $1,918.

Compared with buying on margin

The other way to hold 100 shares with less capital is to buy on margin. Say your broker charges 8% on margin loans: you put up $5,000, borrow $5,000 and pay $400 in interest over the year. If the stock falls to 70, you lose $3,000 plus $400 of interest, and a deeper fall brings a margin call. Of the LEAPS' $735 in time value, only $333 is interest (at the 4% risk-free rate); the other $402 buys the floor. You can lose at most $2,235, and there is no margin call. The trade-offs: option bid–ask spreads are usually wider than the stock's, and LEAPS don't collect dividends.

How to pick them, how to manage them

• Delta 0.70–0.80: go deeper and you pay less time value but tie up more capital, close to just buying the stock; go shallower and time value becomes a bigger share of the price, which is closer to speculation.
• More than a year to expiration; with 4–6 months left, consider rolling to a later expiration to stay out of the stretch where time decay speeds up.
• Watch IV: this LEAPS has a Vega of 0.284, so a 10-point drop in IV costs $284 per contract. Don't buy LEAPS when IV is high.
• Watch dividends: this course assumes no dividends. LEAPS holders don't receive dividends, and calls on dividend-paying stocks are priced lower to match, so include the dividend when you compare.
• Don't lever up the money you saved: B's advantage comes from the cash left over. If you spend the $7,765 you saved on three more LEAPS, you go from “a stock with a floor” to a leveraged position with exposure to about 320 shares.

7.7When options beat stock

Options work better than stock in four situations: you want convexity, you want a capped loss, you are betting ahead of an event, or capital efficiency matters to you. The rest of the time, stock is usually less trouble.

1. Convexity: winning at the extremes

Compare 1 90-day ATM call ($641, Delta 0.556) with 56 shares, which have the same Delta. At expiry:

The crossover points are 88.55 and 114.57: if the stock ends between them, the shares do better; outside them, the option does better. So options suit a view of “either it rallies hard or I admit I'm wrong,” not a view of “it will drift up a little.”

2. Capped loss: a stop order can't help you in a gap

The stock gaps down 30% overnight. 100 shares lose $3,000; a stop order fills at the opening price and can't protect you from the gap. On the same day, the 90-day ATM call falls from 6.41 to 0.04, a loss of $637, and it can never lose more than $641. Even if IV jumps to 45% after the gap, it is worth only 0.47.

3. Before an event: only if you expect a bigger move than the implied one

Take the earnings example from Chapter 6: a 7-day ATM call is worth 4.45 at IV 80%. After earnings IV drops back to 35%; with the stock +10% the call makes 127%, at +5% it makes 21%, at +3% it loses 16%, and on a drop it can lose up to 100%. The stock simply makes 10% on a 10% rise and loses 15% on a 15% drop. Using options to express an event view only makes sense if you have reason to believe this move will be clearly bigger than the roughly 8.8% the market implies, and you accept losing up to the entire premium.

4. Capital efficiency

LEAPS give you about 80% of the exposure for 22% of the capital (Section 7.6); the rest of the money can earn interest or be spread across other positions. For a student account without much money, that means you can express a view on a high-priced stock without margin leverage.

7.8Five common buyer mistakes

Buyers rarely lose money because they got the direction completely wrong. More often it is one of the five mistakes below, all of which can be avoided in advance.

Mistake 1: buying too far out of the money

A 30-day call with a Delta of 0.10 (strike 112) costs only $43 and looks cheap. Its breakeven is 112.43, a 12.4% rise; at IV 30% one standard deviation over a month is only 8.6%, so you need a move of 1.45 standard deviations. The probability of finishing in the money is 9.3%, and of finishing above breakeven 8.6%. It is cheap in dollars but not at all cheap in probability: about nine times out of ten you lose everything.

Mistake 2: buying too short

A 7-day option loses 7% of its value per day, and because decay runs on calendar days, a weekend takes three days' worth. Short-dated options are cheap because they leave you the least time to be wrong.

Mistake 3: buying when IV is high

Table 7-7 already showed this: on the same 5% rise, buying at high IV made only 13%, while buying at low IV made 100%. IV is usually high before earnings, after a big drop and while a hot theme is at its peak.

Mistake 4: positions that are too big

Buyers usually win less than half the time. With a 35% win rate, the chance of 5 losses in a row is 0.65⁵ = 11.6%; the chance of at least one 5-trade losing streak in 50 trades is as high as 92.4%, and the chance of at least one 8-trade losing streak in 100 trades is 69.0%. Losing streaks will come. The question is whether your account can survive them.

Risk 20% per trade and five losses in a row leave you with a third of the account; you would have to triple it just to get back to even. Risk 2% per trade and after 10 losses in a row you still have more than 80%.

Mistake 5: not taking profits

You buy a 60-day ATM call for 5.17. On day 20 the stock is up to 108 and the option is worth 9.63, an 86% gain. You decide to “wait a bit longer.” On day 45 the stock is back at 101 and the option is worth just 3.06, a 41% loss; hold to expiry with the stock at 101 and it is worth only 1.00, a loss of 81%. Had you sold half on day 20 and the other half on day 45, you would still be up 23% overall. Open profits on an option “go bad”: time value drains away every day, and Delta shrinks as the stock pulls back.

7.9Management rules

Before you place the order, write down three exit rules: how much profit gets you out, how much time gets you out, and what level in the underlying gets you out. And size the position on the assumption that “this money could all go to zero.”

Rule 1: take profits at a target

Write down two targets in advance and act on whichever comes first: a return target for the option (say +50% to +100%) or a price target for the underlying (say the stock reaching 110). When one is hit, take at least some profit. If the option has doubled, sell half, and the rest is effectively free. You can also turn the long call into a spread to lock in part of the profit while keeping some exposure (Case 3).

Rule 2: time stop

The first 30 days cost only 19.4%; the last 30 days take all of the remaining 56%. The rule: when the time left falls to a third of the original term (30 days for this option) and your view hasn't started to play out, close or roll. Don't drag the position into the stretch where decay is fastest.

Rule 3: set the stop on the underlying

Option prices are distorted by IV changes, the bid–ask spread and time decay, so a stop based on the option's percentage loss is easily knocked out by noise. A 30-day ATM call with the stock unchanged is down 30% after 15 days; if your stop is −30%, the passage of time alone will trigger it. A sounder approach is to set the stop on the underlying's price: get out at the level where your view is proven wrong (for example, a break below support). A stop on the option's percentage loss can serve as a second line of defense.

Rule 4: be ready for zero

A buyer's maximum loss is the entire premium, and that will happen often. Keep the premium on each trade to 1%–3% of the account, and count multiple trades in the same direction as one. If losing it all would keep you up at night, the position is too big. Also, don't “average down” on a losing option: it is losing time as well as money, and averaging down only makes the next zero bigger.

Turn the rules into a trading plan

Take the 90-day 94 call from Case 1, the contract that fits the view best, in a $50,000 account:

View

Up to 110 within three months

Contract and size

90-day 94 call, 9.84, 1 contract, $984, 2.0% of the account

Profit target

Sell half when the stock hits 110 or the option is up 70%. If the stock reaches 110 by day 45, the option is about 16.75, exactly +70%

Time stop

Close if the stock still isn't above 104 on day 60 (30 days left). If the stock is at 100 then, the option is about 7.39, a 25% loss

Underlying stop

Close if the stock breaks below 95; the view is wrong. If it falls to 95 by day 30, the option is about 5.42, a 45% loss

Worst case

The $984 goes to zero and the account is down 2%

Every number in this plan was worked out before the order went in. While you hold the position, you just follow it; you don't have to make decisions on the fly when the market is at its most stressful.

CasesThree cases

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